Jamie Oliver, the celebrity chef, cookbook author, restaurant supremo, food campaigner “and most importantly today … dad”, has called on David Cameron to be “as brave as he knows he should be” in tackling Britain’s obesity crisis.

Speaking to a committee of MPs on Monday, Oliver said he had “robust” discussions with the prime minister about his proposed introduction of a 20% tax on sugar-sweetened drinks.

Cameron should “frankly, act like a parent” with food manufacturers, Oliver said, adding: “Industry has to be kept in line … When my kid is a little bit naughty, gets a bit lairy, it goes on the naughty step.”

The government is currently reviewing the measures it will include in a forthcoming anti-obesity strategy, and Oliver told the health select committee he did not believe ministers had yet ruled out including the controversial levy, which he says would add around 7p to the price of a 330ml can of fizzy drink.

The tax, he said, would “remind [manufacturers] who is boss. And that is child health and the government.

“We should work out who is running the country. Is it businesses – who are profiting from ill health in our country – or is it us?”

More important than the tax itself, he said, would be the message it sent that the government “is willing to fight tooth and nail for public health, and especially children’s health”.

In an unconventional committee session, the chef pulled props from a plastic bag to illustrate his points and handed them round to committee members, the press and audience.

“If you can just hold that up, Helen …” he said at one point to Helen Whateley, the Conservative MP for Faversham and Mid Kent, referring to a bottle of fizzy drink whose wrapper he had doctored to include the number of teaspoons of sugar it contains.

“The reason the industry don’t want you to have that is because the impact is visceral,” said. “I’m not saying you ain’t going to buy it, I’m saying you won’t rattle it out three times a day.”

Just what the doctor ordered: Jamie Oliver declares war on sugar

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For the benefit of the stenographers “and those following on Hansard”, Sarah Wollaston, the committee chair, stepped in to explain what was happening.

Oliver has published a five-point sugar manifesto in which, alongside the 20% tax, he calls for televised junk food advertising to be banned before 9pm, traffic light labelling to be made mandatory, and for the introduction of an additional compulsory labelling system showing sugary drinks’ sugar content in teaspoons. He also wants the currently voluntary “responsibility deal” on public health to be made mandatory.

Lifting a can of Red Bull from his bag, Oliver also raised the possibility of minimum age standards for young children purchasing drinks heavy in sugar and caffeine from corner shops. “We’ve got to get medieval on this stuff,” he said.

Oliver told MPs he had seen consumption of sugary drinks falling in his own chain of 46 restaurants, which have already imposed a tax of 10p, with the money raised going to programmes aimed at improving children’s health.